Answer:
19272 feet
Step-by-step explanation:
We are given that the distance between the person and peak is 5 miles.
and angle is [tex]47^\circ[/tex] when we look up at the mountain peak.
The given situation is best represented as a right angled triangle as shown in the attached figure.
[tex]\triangle[/tex]IKJ where [tex]\angle K = 90^\circ[/tex]
IK is the mountain.
J is the point where we are standing.
Distance JI = 5 miles
[tex]\angle J = 47^\circ[/tex]
To find: Distance IK = ?
We can use trigonometric identities to find IK.
[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]sinJ = \dfrac{IK}{JI}\\\Rightarrow sin47 = \dfrac{IK}{5}\\\Rightarrow IK = sin47^\circ \times 5\\\Rightarrow IK = 0.73 \times 5\\\Rightarrow IK = 3.65\ miles \\\Rightarrow IK = 3.65 \times 5280\ ft\\\Rightarrow IK = 19272\ ft[/tex]
Hence, height of mountain = 19272 ft
